Problem 26 - Chemistry The Central Science

Question

For the following processes, calculate the change in internal energy of the system and determine whether the process is endothermic or exothermic: (a) A balloon is cooled by removing 0.655 \(\mathrm{kJ}\) of heat. It shrinks on cooling, and the atmosphere does 382 J of work on the balloon. (b) A 100.0 -g bar of gold is heated from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\) during which it absorbs 322 \(\mathrm{J}\) of heat. Assume the volume of the gold bar remains constant.

Step-by-Step Solution

Answer

Process (a): - Change in internal energy: ∆U = -273 J - The process is exothermic Process (b): - Change in internal energy: ∆U = 322 J - The process is endothermic

Step 1: Process (a): Calculate the change in internal energy (∆U)

Using the first law of thermodynamics, ∆U = Q - W, we know the heat transfer (Q) and work (W) done on the balloon. In this case, Q = -0.655 kJ (since heat is removed) and W = -382 J (given that work is done on the balloon). First, we need to convert kJ to J: Q = -0.655 kJ × \(1000 \frac{J}{kJ}\) = -655 J. Now we can calculate ∆U: ∆U = Q - W = (-655 J) - (-382 J) = -655 J + 382 J = -273 J.

Step 2: Process (a): Determine whether the process is endothermic or exothermic

As we calculated the change in internal energy, ∆U, as negative (-273 J), this process implies a net loss of internal energy, which signals an exothermic process.

Step 3: Process (b): Calculate the amount of heat transfer required to heat the gold bar

We are given the initial (25°C) and final (50°C) temperatures of the gold bar and the heat absorbed by the bar (Q) is 322 J. The volume of the gold bar remains constant during heating, so no work is done during the process (W = 0).

Step 4: Process (b): Calculate the change in internal energy (∆U)

Before determining if the process is endothermic or exothermic, we calculate ∆U using the first law of thermodynamics, where W = 0: ∆U = Q - W = 322 J - 0 = 322 J.

Step 5: Process (b): Determine whether the process is endothermic or exothermic

With a positive change in internal energy (∆U = 322 J), this process is an endothermic process, as the gold bar gained internal energy. To summarize: Process (a): - Change in internal energy: ∆U = -273 J - The process is exothermic Process (b): - Change in internal energy: ∆U = 322 J - The process is endothermic

Key Concepts

Change in Internal Energy

Understanding the change in internal energy of a system is crucial in the study of thermodynamics. This concept is often denoted as \( \Delta U \) and it signifies the difference between the energy put into (or added to) the system and the energy that the system loses to the surroundings. In physics, this can be represented mathematically by the first law of thermodynamics, which essentially states that \( \Delta U = Q - W \), where \( Q \) is the heat exchange between the system and its surroundings, and \( W \) is the work done by or on the system.

For example, when a balloon is cooled and heat is removed, it contracts and the atmosphere does work on it. This leads to a reduction in the balloon's internal energy, hence a negative \( \Delta U \) value, as observed in the given exercise. In this case, the system (the balloon) ends up with less energy than it started with because the energy that leaves the system as heat exceeds the energy entering as work performed on the system.

Endothermic and Exothermic Processes

These processes are the bedrock for understanding how energy transformations govern physical changes. An endothermic process is characterized by the absorption of heat. Here, the system gains energy from its surroundings, usually in the form of heat, resulting in a positive \( \Delta U \). It's akin to a sponge soaking up water; the system 'soaks up' energy. On the other hand, an exothermic process releases heat, leading to a negative \( \Delta U \) because the system loses energy to its surroundings.

In our exercise, cooling the balloon, which resulted in a negative \( \Delta U \), signifies an exothermic process as the system releases energy. Conversely, heating the gold bar causes it to absorb heat, making it an endothermic process indicated by a positive value of \( \Delta U \).

Heat Transfer

This phenomenon involves the movement of thermal energy from one object or body to another. Heat transfer occurs in various forms, such as convection, conduction, and radiation. In the context of our exercise, when the balloon is cooled, there is a transfer of heat from the balloon to its cooler surroundings. Similarly, as the gold bar is heated from \(25^\circ C\) to \(50^\circ C\) and absorbs heat, this is also a transfer of energy but into the system.

It's important to note that heat transfer is always from a higher temperature body to a lower temperature one, which is a fundamental concept of thermodynamics. In our calculations, heat absorbed by the system is considered as positive (\( Q > 0 \) ), while heat released by the system is negative (\( Q < 0 \) ).

Thermodynamics

This branch of physics deals with the relationships between heat and other forms of energy. The core of thermodynamics is formed by its laws, which describe how energy is conserved and converted. In particular, the first law of thermodynamics, also known as the law of energy conservation, asserts that energy cannot be created or destroyed in an isolated system. Instead, it can only change from one form to another.

In our scenario, whether cooling a balloon or heating a gold bar, these processes can be analyzed within the framework of thermodynamics, giving us valuable insights into how energies are transformed. In the educational context, thermodynamics is not just a topic within physics; it's a lens through which we can interpret many natural phenomena and technological processes.